2s - 1 THE UNIVERSITY OF HONG KONG FACULTY OF BUSINESS AND...

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Unformatted text preview: 1 THE UNIVERSITY OF HONG KONG FACULTY OF BUSINESS AND ECONOMICS FINA0301CDE - DERIVATIVES First Semester, 2009-2010 Tutorial 2 Problem Set Solution Chapter 3 c Practice Questions Question 1 A bull spread is created by buying the $30 put and selling the $35 put. This strategy gives rise to an initial cash inflow of $3. The outcome is as follows: Stock Price Payoff Profit S T 35 0 3 30 S T < 35 S T- 35 S T 32 S T < 30 -5 -2 A bear spread is created by selling the $30 put and buying the $35 put. This strategy costs $3 initially. The outcome is as follows: Stock Price Payoff Profit S T 35 0 -3 30 S T < 35 35 - S T 32 - S T S T < 30 5 2 Question 2 The bull spread is created by buying a put with strike price K 1 and selling a put with strike price K 2 . The payoff is calculated as follows: Stock Price Range Payoff from Long Put Option Payoff from Short Put Option Total Payoff S T K 1 0 0 0 K 1 < S T < K 2 0 S T K 2 - ( K 2 S T ) S T K 1 K 1 S T S T K 2 - ( K 2 K 1 ) FINA0301 Tutorial 2 Solution Mr. Clive Man Chung HO 2 Question 3 (i) Payoff: If we buy the index, we receive at the time of expiration T of the options simply S T . The payoffs of part (ii) are a little bit more complicated. If we deal with options and the maximum function, it is convenient to split the future values of the index into two regions: one where S T < K and another one where S T K . We then look at each region separately, and hope to be able to draw a conclusion when we look at the aggregate position. (ii) We have for the payoffs in (ii): Instrument S T < K= 950 S T K = 950 Get repayment of loan $931.37 1.02 = $950 $931.37 1.02 = $950 Long Call Option max ( S T- 950, 0) = 0 S T-950 Short Put Option - max (950 - S T , 0) 0 Total S T-1020 S T-1020 FINA0301 Tutorial 2 Solution Mr. Clive Man Chung HO 3 We now see that the total aggregate position only gives us S T , no matter what the final index value is the same payoff as in part (i). Our proof for the payoff equivalence is complete....
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This note was uploaded on 01/26/2010 for the course FINA 2802 taught by Professor Xia during the Fall '09 term at HKU.

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2s - 1 THE UNIVERSITY OF HONG KONG FACULTY OF BUSINESS AND...

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